i am struggling with this multiplication sequence proof.
Problem: Prove by induction that:
$\prod_{i=1}^{n} (3 - \frac{3}{i^2})$ = $\frac{3(n+1)}{2n}$
This is my attempt or what I am thinking:
$\prod_{i=1}^{n} (3 - \frac{3}{i^2})$ is basically -> $3 -$ $\frac{3}{n^2}$
So then P(n) should become: $3 -$ $\frac{3}{n^2}$ = $\frac{3(n+1)}{2n}$
But then i get an issue with step 1.
So step1: Show that P(1) is true
What i get is: $3 - 3 = \frac{3(2)}{2}$ Which is: $0 = 3$ Which is false..
What am i doing wrong and how should i proceed to prove this?? I tried writing out the sequence, but then the multipilication begins with $0 * \frac{9}{4} * ... * (3 -\frac{3}{n^2})$ . Maybe i am mixing stuff up with the addition sequences??
You are right, the product is always zero as written. On the other hand, if you start from $i=2$ all is well.